Tristable phenomenon in a predator-prey system arsing from multiple limit cycles bifurcation

In this paper, we consider a predator-prey system with Holling type III ratio-<br>dependent functional response. Such a system can exhibit complex dynamical<br>behavior such as bistable and tristable phenomena which contain equilibria<br>and oscillating motions for certain parameter values. In particular, we show<br>that the ratio-dependent predator-prey system can exhibit multiple limit<br>cycles due to Hopf bifurcation, giving rise to co-existence of stable equilibria<br>and stable periodic solutions. These solutions may reveal some new type of<br>patterns of complex dynamical behaviors in predator-prey systems.